Method and Apparatus for Locating a Parallel Arc Fault

ABSTRACT

Methods to determine the location of an arc fault include a first method utilizing the inherent resistance per unit length of the wire. A second and a third method utilize an inherent inductance per unit length of the wire. The second method derives the inherent inductance from the output voltage and a rate of current rise. The third method derives the inherent inductance from a resonant frequency of an oscillating current. The information is useful to locate a fault emanating from a wire member of a wiring harness used to distribute power about an aircraft.

CROSS REFERENCE TO RELATED APPLICATION(S)

This patent application is a division of U.S. patent application Ser.No. 12/583,396, titled “Method and Apparatus for Locating a Parallel ArcFault,” that was filed on Aug. 19, 2009. The disclosure of that patentapplication is incorporated by reference in its entirety herein.

U.S. GOVERNMENT RIGHTS

N.A.

BACKGROUND

1. Field

This invention relates to methods and systems to determine the locationof an arc fault between adjacent wires in a wiring harness, such as usedto provide power to widely separated locations and components on anaircraft. More particularly, by utilizing length dependent properties ofthe wires, such as resistance and inductance, the distance to a remoteparallel arc-fault may be calculated.

2. Description of the Related Art

Aircraft require electrical power delivered to widely separatedlocations throughout the aircraft. Flight crucial circuits includeexternal lighting, instrument panels and communications. Non-flightcritical circuits include in-flight entertainment systems and galleys.One or more generators on the plane satisfy the aircraft electricalsystem requirements and typically produce 115 volts AC, 400 hertz. Somepresent day electrical components utilize 28 volts DC. Other voltagerequirements, such as 270 volts DC and variable frequencies, are beingconsidered for future aircraft. The electrical power is delivered fromthe generators to the electrical systems through wiring harnesses thatcontain bundles of wires. Such harnesses may include in excess of 50wires and have wires of variable lengths, from under 5 feet up toseveral hundred feet in length.

The bundled wires are individually coated with a polymer insulator, suchas polyimide. Over time, and due to environmental factors such as heat,the insulation may wear away or crack exposing an encased conductor. Iftwo conductors are exposed in close proximity, an electric current mayarc from one conductor to the other. Arcing may also occur between asingle exposed conductor and the airframe. This type of fault isreferred to as a parallel arc fault. Arcing can degrade insulation ofadjacent wires and is a fire hazard. Therefore, it is necessary tosuppress the arc as quickly as possible. Thermal circuit breakers weredeveloped to protect the wire insulation on aircraft from damage due tooverheating conditions caused by excessive over-current conditions. Thethermal circuit breakers are generally not effective to protect againstan arc fault. The arc fault is often an intermittent problem occurringduring a specific condition, such as in-flight vibration of an aircraftframe. The arc is transient, frequently on the order of milliseconds,such that a current overload and thermal increase does not occur,rendering a thermal circuit breaker ineffective.

A circuit interrupter that detects an arc fault and interrupts the flowof current is disclosed in U.S. Pat. No. 5,682,101 to Brooks, et al. Thepatent discloses a method to detect an arc fault by monitoring the rateof change of electrical current as a function of time (di/dt) andgenerating a pulse each time di/dt is outside a predetermined threshold.An arc fault signal is sent to a circuit breaker or other safety deviceif the number of pulses per a specified time interval exceeds athreshold. U.S. Pat. No. 5,682,101 is incorporated by reference in itsentirety herein.

An electronic circuit breaker that detects arc faults enhances aircraftsafety, but does not assist in determining the location of the fault.Wiring bundles on an aircraft may extend for several hundred feet andare typically inaccessible, such as under floorboards or extendingthrough wing struts. Locating a fault is time consuming and requiresconsiderable effort to access the wire bundle. U.S. Pat. No. 7,253,640to Engel, et al. discloses a method to determine a distance to an arcfault that employs the value of the peak arc current, the wireresistance per unit length, and a nominal peak line to neutral voltagevalue. A constant arc voltage or an arc voltage as a function of thevalue of the peak current is then provided to calculate the distancefrom the arc fault detector to the arc fault. U.S. Pat. No. 7,253,640 isincorporated by reference in its entirety herein.

Using wire resistance to locate an arc fault is of limited value. Themagnitude of resistance of the wires is typically in the milliohm rangewhile the resistance of the arc is unpredictable and variable and can befrom zero to tens of ohms. As a result, this method is prone to largeerror.

There remains, therefore, a need for a method and system to moreaccurately locate an arc fault to thereby more readily facilitate repairof damaged insulation and wires.

BRIEF SUMMARY

The details of one or more embodiments of the disclosure are set forthin the accompanying drawings and the description below. Other features,objects and advantages will be apparent from the description anddrawings, and from the claims.

It is an object to provide herein methods and systems for determiningthe location of an arc fault, such as emanating from a wire member of awiring harness of an aircraft. A first method utilizes an inherentresistance per unit length of the wire. Second and third methods utilizean inherent inductance per unit length of the wire. The second methodderives the inherent inductance from the output voltage and a rate ofcurrent rise. The third method derives the inherent inductance from aresonant frequency of an oscillating arc current.

The first method includes the steps of measuring a distance to an arcemanating from the wire by obtaining an output voltage and a peakcurrent, calculating a resistance of the wire up to the arc fromR_(wires)=V₀/I_(arc(peak)) and then utilizing an inherent resistance perunit of length of the wire to determine a distance to fault.

The second method includes the steps of measuring a distance to an arcemanating from the wire by obtaining an output voltage and a rate ofcurrent rise as a function of time, di/dt, calculating an inductance ofthe wire from L_(wire)=V_(source)/(di/dt) utilizing an inherentinductance per unit of length of the wire to determine a distance tofault.

The third method includes the steps of measuring a distance to an arcemanating from the wire by isolating the voltage source from the wirewith a decoupling inductor, inserting an output capacitor between thedecoupling inductor and a load, measuring a resonant frequency of acurrent oscillating around a loop defined by the output capacitor, theinductance of the wire, the arc and a ground, calculating an inductanceof the wire up to the arc and utilizing an inherent inductance per unitof length of the wire to determine a distance to fault.

A system to utilize the third method includes a voltage source, a load,a wiring harness having a plurality of parallel running insulated wireswith at least one of the plurality of wires electrically interconnectedto the voltage source and to the load. A decoupling inductor is disposedbetween the voltage source and the wiring harness and is effective toprovide RF isolation of the voltage source from the wiring harness. Anoutput capacitor is disposed between the decoupling inductor and thewiring harness. An output buffer is effective to store data related to awaveform oscillating around a loop defined by the output capacitor, thewire, an arc bridging the wire and a ground, and the ground return.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates in cross-sectional representation an aircraft wiringharness as known from the prior art.

FIG. 2 illustrates a parallel arc fault between two wires containedwithin the wiring harness of FIG. 1.

FIG. 3 is a circuit model of a parallel arc fault for detection by wireresistance measurement in accordance with a first embodiment.

FIG. 4 is block diagram of a system to locate an arc fault detected bythe wire resistance method.

FIG. 5 is a circuit model of a parallel arc fault for detection bychange in current (di/dt) as a factor of time in accordance with asecond embodiment.

FIG. 6 is block diagram of a system to locate an arc fault detected bythe di/dt method.

FIG. 7 is a circuit model of a parallel arc fault for detection byinductance-capacitance-resistance (LCR) oscillation in accordance with athird embodiment.

FIG. 8 is block diagram of a system to locate an arc fault detected bythe LCR oscillation method.

FIG. 9 illustrates di/dt as a function of the distance to fault inaccordance with the second embodiment.

FIG. 10A illustrates the percent error in the computation of distance tofault from FIG. 9 when R_(arc) is 1 ohm and FIG. 10B illustrates thepercent error when R_(arc) is 2 ohms.

FIG. 11A illustrate a waveform from the second embodiment when R_(arc)is about zero and FIG. 11B illustrates a waveform when R_(arc) is 7.5ohms.

FIG. 12 illustrates frequency as a function of the distance to fault inaccordance with the third embodiment.

FIG. 13 illustrates the percent error in the computation of distance tofault from FIG. 12 when R_(arc) is 0 ohm.

FIG. 14A graphs arc current, arc voltage and source voltage for a 19foot distance to fault and FIG. 14B graphs those parameters for a 25foot distance to fault.

FIG. 15A illustrates oscillation damping when the arc resistance is 7.5ohms, FIG. 15B when the arc resistance is 15 ohms and FIG. 15C when thearc resistance is 30 ohms.

FIG. 16 is a waveform illustrating arc current and arc voltage for a 19foot distance to fault.

FIG. 17 is a waveform illustrating irregular arc voltage.

FIG. 18 is a fast fourier transform (FFT) analysis of the waveform ofFIG. 14B.

FIG. 19 is a fast fourier transform analysis of the waveform of FIG.15B.

FIG. 20 is a waveform illustrating rapid voltage noise prior tooscillation.

FIG. 21 is a waveform illustrating rapid voltage noise around theresonant frequency.

FIG. 22 is a waveform illustrating a relatively weak signal.

Like reference numbers and designations in the various drawingsindicated like elements.

DETAILED DESCRIPTION

FIG. 1 illustrates a wiring harness 10 in cross-sectionalrepresentation. A restraining band 12 supports a bundle of wires 14.Each wire 14 has an electrically conductive core 16 sheathed in anelectrically insulating jacket 18. Typically, the jacket 18 is apolymer, such as a polyimide. The bundle may contain in excess of fiftywires 14.

With reference to FIG. 2, the bundles of wires 14 extend throughout theaircraft and deliver power to widely separated systems and components.The lengths of wires in the bundles may be from under five feet to inexcess of several hundred feet. The bundles travel in areas where spaceis available, areas frequently having limited accessibility, such asbetween a cabin floor 20 and a ceiling 22 of a cargo hold. Individualwires 14′ separate from the bundle at required locations. For example,the wire 14′ may provide power to an in-seat power supply unit for an inflight entertainment system.

If the insulating jackets 18 fail on two wires 14 in proximity, an arcfault may occur. While an electronic circuit breaker, as known from theprior art, is effective to stop the flow of current in the affectedwires, locating the fault and repairing the fault in a potentiallyinaccessible location has, until now, proven difficult. Following arethree methods and systems to locate the fault and facilitate repair.

A first method to estimate the location of an arc fault utilizes wireresistance. A circuit modeling the harness is illustrated in FIG. 3 andFIG. 4 is a block diagram of a system to locate an arc fault by the wireresistance method.

The resistance of the wiring harness represented by R_(wire) 24 is thetotal of all resistance in series with the arc 26. If the arc 26 is tothe airframe 28, than it is the resistance of the single wire that isarcing, as shown in FIG. 3. If the arc is between two wires, theresistance is the total resistance of both wires. Uncertainty of thetotal resistance is one reason a resistance measurement system isinaccurate.

The resistance of the arc represented by R_(arc) 30;

The voltage of the source 32, e.g. generator output, is represented byV_(source);

The in-series resistance of the electronic circuit breaker (ecb) and thevoltage source is represented by R_(source)+R_(ecb).

The resistance of the wire relates the current and the voltage by Ohm'slaw:

R _(wire) =V _(o) /I _(arc(peak))   (1)

Where I_(arc(peak)) is peak measured current in the circuit and V_(o) ismeasured output voltage of the electronic circuit breaker 34. Thedistance to fault (DTF) is then the measured value for R_(wire) 24divided by the inherent resistance per unit of length value for the wiregauge and composition.

Error in the circuit model of FIG. 3 comes from the unknown arcresistance 30 that created voltage drop V_(arc) across it. In an idealscenario, the voltage drop across the wires is equal to the V_(o).However in reality, the arc resistance 30 will cause V_(o) to be dividedbetween V_(wire) and V_(arc) introducing an error. When I_(arc) is at amaximum we can assume that arc resistance is at a minimum and most ofthe V_(o) is dropped across the R_(wire) reducing this error term to aminimum. The percent error in a DTF calculation is given by:

% Error=(I _(arc) *R _(arc) /V ₀)*100%   (2)

or as a ratio of resistances:

% Error=(R_(arc)/R_(wire))*100% (3)

The magnitude of R_(wire) 24 is typically in milliohms range whileR_(arc) 30 is unpredictable and variable between 0 ohm and tens of ohms.Because of this possible error range, this method has limited use. Themethod can, however, be used to do an initial prediction where a faultmight be located. If the peak arc current is large enough where it canactually be caused by resistance of the installed harness, an assumptioncan be made that the arc resistance 30 is 0 ohm. This typically is abrief condition that can occur during the arc fault when the faultyconductors briefly weld themselves together. Fast response point of theECB 34 can also be used to predict the section of the wire where thefault occurred. If arc resistance 30 is at 0 ohms, every wire gauge willhave a critical length for which hard faults will always result in anI²t (a common rating value for circuit breakers where I is current and tis time) trip and never a fast response loop. This information can beused to predict where the fault is located.

A second method to estimate the location of an arc fault 26 utilizesinductor di/dt 36. A circuit modeling the harness with the wireinductance L_(wire) 38 and wire resistance R_(wire) 24 in series isillustrated in FIG. 5. FIG. 6 is a block diagram of the system to locatean arc fault by the inductor di/dt method. The system is similar to thatillustrated in FIG. 4 for the wire resistance method except that themicroprocessor 40 does a different set of calculations using the samebasic data.

R_(arc) 30 is the resistance of the arc 26.

V_(source) is the source 32 voltage.

R_(source) is the source 32 resistance.

R_(ecb) is the resistance of an electronic circuit breaker 34.

R_(source)+R_(ecb) are in series resistance of the circuit breaker andthe voltage source.

Before a parallel arc fault event, an initial condition is establishedby the current flowing from the source 32 into the load 42. When an arc26 strikes at some distance from the circuit breaker 34, it forms aclosed loop defined by L_(wires), R_(wires), R_(arc), V_(source),R_(source) and R_(ecb). The circuit can be described by analyzing a stepresponse typical of an LR circuit. Due to the influence of L_(wires),the arc current does not rise to its final value instantaneously. Therate of current rise, di/dt 36, is a function of inductance and voltagedrop across L_(wires):

L _(wires) =V _(source) (di/dt)   (4)

Or

di/dt=V _(source) /L _(wires)   (5)

A more accurate equation takes into account the voltage drop associatedwith its series resistance:

V _(source) −i(t)R _(source) −i(t)R _(ecb) i(t)R _(wire) −i(t)R _(arc)=L _(wires) *di/dt   (6)

where:

i(t) is current flowing through the harness at time, t.

R_(arc) is resistance of an arc 26 when the arc strikes.

As a first order approximation, we assume that R_(ecb) and R_(source)are sufficiently low so that V_(source)=V_(o).

We can also assume that R_(wires)<<R_(arc) and can be approximated to be0 ohms.

The equation for the inductance of the wires 38 is then given by:

L _(wires)=(V _(source) −i(t)R _(arc))/(di/dt)   (7)

In the absence of R_(arc) 30, the rate of current rise di/dt 36 issimply a ratio of V_(source)/L_(wires). However, resistance of an arc 30is an unknown and unpredictable value resulting in an error term in theequation given by i(t)R_(arc) as a voltage drop across the arc 26itself. The instant when the switch closes the original steady stateI_(load) current is maintained through the arc setting the initialcondition. That current will establish initial voltage drop across thearc resistance 30. The actual current I(t) is given by:

I(t)=(V _(source) /R _(arc))+(I _(load)−(V _(source) /R _(arc)))exp(R_(arc) /L _(wires))*t   (8)

and the actual di/dt is given by:

di/dt=((V _(source) −R _(arc) *I _(load))/L _(wires))exp(R _(arc) /L_(wires))*t   (9)

di/dt is dependent on the length of the closed loop, one segment ofwhich is the arc fault. Therefore, knowing di/dt enables a calculationof the DTF by calculating the inductance of the fault loop:V_(source)×dt/di=L_(wire). For a particular wire gauge and type, thereis a constant inductance per linear foot, K (μH/ft). Then calculate thedistance to the fault: DTF=½(L/K).

As seen from the equations, the actual rate of current rise in thecircuit is not a constant value, rather the current increasesexponentially approaching V_(source)/R_(arc) as final value. A percenterror in distance to fault calculations can be thought of as thedifference between expected and actual voltage across L_(wires). Thatdifference is the voltage across R_(arc). If V_(source) is the expectedvoltage drop when R_(arc)=0 ohm, then:

% Error=−(i(t)R _(arc))/V _(source))*100%=[((V _(source) −R _(arc) *t_(oad))exp(R _(arc) /L _(wires))*t)/V _(source)]*100%   (10)

Percent error in measuring di/dt and thus in distance to faultcomputation depends on several variables: the resistance of the arc,initial load current and time of measurement. Resistance, R_(arc), canbe viewed as the sum of every in-series resistance shown in Equation 6for more accurate error prediction.

A third method to estimate the location of an arc fault utilizes theresonant frequency of LCR oscillation. A circuit modeling the harness 10with oscillating circuit 44 is illustrated in FIG. 7. FIG. 7 shows asimplified schematic of the source 32, electronic circuit breaker 34,harness 10 and load 42 system. L_(decoupling) is an output inductor 46at the output of the circuit breaker 34 that serves as a decouplingelement separating in frequency the source 32 from the harness 10(L_(decoupling)>>L_(wires)) at high frequencies. Before the parallel arcfault event 26 strikes, there is an initial steady state condition wherethe load 42 draws current from the source 32 (I_(load)). At this point,the output capacitor 48 of the circuit breaker 34, C_(out) is fullycharged to the V_(o) voltage. When the arc 26 strikes, an LCR loop isformed by C_(out), L_(wires), R_(wires)+R_(arc). Due to the presence ofthe output inductor 46, the circuit to the left of V_(o) is effectivelydecoupled from an AC perspective.

At this instant we can examine the portion of the circuit formed byC_(out)-L_(wires)-R_(wires)-R_(arc) only. Output capacitor 48 C_(out)starts to transfer stored energy via in-series resistance R_(wires) andR_(arc) to the inductor 50 formed by L_(wires). When all the storedenergy is transferred to the inductor 50, the inductor 50 starts tocharge back the output capacitor 48 with opposite polarity. The cyclecontinues creating an oscillating current 44 that decays exponentiallydue to the presence of R_(wires) and R_(arc). The frequency of thisoscillation is a function of L_(wires) and C_(out). The resonantfrequency range is set by the initial value of the output capacitor 48.The higher the initial value, the lower the resonant frequency range.While higher frequency ranges are advantageous, providing greatersensitivity (change in frequency per foot) and longer oscillation time,the advantages come at the expense of increased hardware complexity.Also, a smaller initial value may increase the effect of an errorintroduced by parasitic capacitance of the harness 10. An exemplaryinitial value for the output capacitor is between 1 and 15 nF and apreferred range is between 2 and 5 nF.

Oscillating circuit 44 behavior can be described by analyzing thenatural response of a typical LCR circuit. Damping factor, a, idealresonant frequency ω_(o) and damped resonant frequency ω_(d) (actualresonant frequency adjusted from ideal due to damping factors) are givenby:

ω_(o)=1/(L _(wires) *C _(out))^(0.5)   (11)

α=(R _(wires) +R _(arc))/(2*L _(wires))   (12)

ω_(d)=(ω_(o) ²+α²)^(0.5)   (13)

Under-damped oscillation will occur if the combined in-series resistanceof the wires 24 and of the arc 30 is less than the critical resistancevalue:

ω_(o) ²>α²   (14)

or

(R _(wires) +R _(arc))<2*(L _(wires) /C _(out))^(0.5)   (15)

For the typical length wire contained in wiring harness 10, resistance24 is in milliohms range and can be omitted from equation 15 causing thearc resistance 30 value to be the decisive factor whether or notoscillation will occur. We estimate the worst case value for the rightside of the inequality to be somewhere around 7.5 ohms (assuming theoutput capacitance 48 to be no more than 0.1 μF and the minimum wireinductor 50 to be 1.4 μH) which is about 5 feet of AWG 14 wire. Theworst case arc resistance 30 must be less than that to satisfy theequation.

Equations for the current and voltage in the under-damped LCR circuitare given by:

I _(osc)(t)C _(l) e ^(−αt) cos(ω_(d) t)+C ₂ e ^(−αt) sin(ω_(d) t)   (16)

V₀ =I _(osc)(t)(R _(wire) +R _(arc))+L _(wire) *dI _(osc) /dt   (17)

Constants C₁ and C₂ are set from the initial current condition in thecircuit. At the time t=0, current through the wire inductor 50 isI_(load) setting the constant C₁ equal to I_(load). C₂ can be found bytaking a derivative of the I_(osc)(t) and equating that to the(dI_(osc)/dt) from the voltage Equation 17 at the instant when outputcapacitor 48 starts discharging into wire inductor 50. At this instantvoltage V_(o)−(R _(wire)+R_(arc))I_(load) is dropped across the wireinductor 50 and series resistance 24, 30 producing:

C ₂=(V ₀−(R _(wire) +R _(arc))*I _(load))/α*L _(wire)   (18)

Where [(R_(wire)+R_(arc))*I_(load)] is an initial voltage across thewire and the arc resistance 30 is at the instant the arc strikes. Thisvoltage is a result of initial steady state I_(load). Another usefulparameter is the total time of the oscillation as amplitude drops to 10%of the initial maximum. This is found by setting the damping coefficientequal to 0.1 and solving for time t (0.1=e^(−αt)).

t _(max-10%)=4.6L _(wire)/(R _(wire) +R _(arc))   (19)

Unlike the method for locating a fault using inductor di/dt describedabove, as seen from Equation 16, in the present method the frequency ofoscillation does not depend on initial load current I_(load) or timemeaning that the DTF may be accurately determined by the resonantfrequency. Using fixed value output capacitor 48 of the ECB 34 as C andsolving for L, wire inductance, =(1/ω)²)/C. As with the di/dt method,for a particular wire gauge and type, there is a constant inductance perlinear foot, K (μH/ft). Then calculate the distance to the fault:DTF=½(L/K). The percent error in resonant frequency introduced by thearc resistance 30 can be estimated from the difference between idealresonant frequency ω_(o) and the actual resonant frequency ω_(d):

% Error=100%*[(ω_(d) −ω ₀)/ω₀=100%*{[1−(C _(out) *C _(arc) ²)/4L]^(0.5)−1}  (20)

Constraints in the design of hardware for utilizing the LCR oscillationmethod include:

LCR oscillation event happens once, in a brief time period <50 μS. Thecircuit must be ready to respond and process the signal first.

LCR oscillation event happens much earlier than actual electroniccircuit breaker trip. It is preferred to have a reliable way torecognize and trigger on the event prior to an ECB 34 trip.

The circuit must be able to process frequencies of at least 3 Mhz. Anability to process higher frequencies is beneficial.

Preferably, the waveforms may be stored for diagnostic purposes.

Digitizing, storing and processing the waveform offers a potentialsolution. Once the waveform is digitized and stored in the memory it canbe processed at a later time when a relatively slow host processor isready to analyze the data (e.g. when the electronic circuit breaker 34is tripped and the host processor is idle again). A system block diagramis shown in FIG. 8. The output capacitor 34 sets the frequency range ofoperation. The signal is first filtered with an analog bandpass filter52 that is tuned to a frequency range where LCR oscillation is expectedto occur, such as in the range of between 585 kHz and 3 MHz. This filter52 also serves as an antialiasing filter before an A/D converter 54.Output of the bandpass filter 52 is fed into the A/D converter 54constantly sampling at 6-10 Ms/s. The A/D converter 54 writes directlyinto a circular buffer memory without requiring processor involvement.

In a worst case scenario circular buffer 56 must be large enough tostore the waveform data from the instant the arc 26 occurs to the timewhen the ECB 34 recognizes the event and trips. At this point the eventtrigger 58 will send a stop signal 60 to the A/D converter 54. This timewindow can be anywhere from tens of microseconds to hundreds ofmilliseconds depending on the fault conditions. At the 6 Ms/s rate, a 10bit A/D converter 54 will constantly deliver 750 kBytes of data forevery 100 ms into the circular buffer 56 to be processed in the event oftrip. For a 10 Ms/s rate, that number will double.

Another approach is to implement an analog event trigger 58 circuit thatwill stop 60 the A/D converter 54 independent of microprocessor 40 whenLCR oscillation 44 is detected. This circuit can be as simple as arectifier, averager/integrator and a comparator that will constantlymonitor the output of the band pass filter 52. Reducing the trigger timewill reduce the total waveform sample size. As soon as themicroprocessor 40 is ready to process the data, it will use a built inalgorithm (such as fast fourier transform analysis (FFT) with ability tolocate frequency peaks) to perform the distance to fault (DTF)evaluation and transfer the waveform data to an external host as needed.

Success of the methods described above in locating an arc fault in realtime depends on the arc fault event itself, magnitude of R_(arc) and arcvoltage. The percent error in method two, utilizing inductor di/dt, is afunction of initial load current, resistance of the arc and time. WhenR_(arc) is approximately 0 ohms, the expected vs. measured di/dt waswithin 2% error indicating that this method will work if R_(arc) isclose to 0 ohms or when conductors are briefly welded together toproduce low section feeding into the electronic circuit breaker thatadds inductance as well as any internal inductors that are in serieswith the harness.

Unlike the first method, utilizing wire resistance, and the secondmethod, an apparent advantage of method three, utilizing the resonantfrequency of LCR oscillation, is that the distance to fault computationdepends less on resistance of an arc and does not depend on loadcurrent, time or wire sections feeding to the electronic circuitbreaker. From the experimental data that follows, we conclude thatmethod three offers the most potential as a solution for real timedistance to fault measurements. However, it is also the most complex ofthree to implement.

The first method is the easiest to implement. But since with this methodof distance to fault determination depends only on resistance of thewires, a significant error can potentially be introduced by the unknownarc resistance that falls in series with the resistance of the wires.Despite that, this technique can still be used to initially predict thedistance range or section of the wire where the fault is located byusing the peak current draw during the arc fault event to report one ofthe two possible outcomes: fault occurred within critical distancelength of the wire or fault location is uncertain. Minimum hardware, ifany at all, changes would be required to implement the first method intoa current electronic circuit breaker.

Advantages of the methods and systems described above will become moreapparent from the Examples that follow:

EXAMPLES Example 1 Wire Resistance Method

The data below was collected to determine the critical wire length pointfor different wire gauges and electronic circuit breakers fast trippoints. The fast response trip point was set at 10× and the inputvoltage set at 28V DC. The critical length point of the wire is deriveddirectly from the resistance value beyond which the short circuitcurrent drops below the 10× rating of the circuit breaker. This pointcan be defined as a critical resistance.

R_(critical resistance) =V ₀/10×ECB Rating   (21)

Critical length of the wire with given AWG can be calculated by:

Critical Length=R _(critical 0) /R per unit length   (22)

Resistance per unit of length is a characteristic of a wire having agiven AWG. Table 1 shows some Critical Resistance and Critical Lengthvalues for ECBs and measured wire gauges.

TABLE 1 ECB Resistance per Critical Critical Rating Gauge ft. ResistanceLength (Amps) (AWG) (mOhms/ft) (Ohms) (ft) 2.5 18 6.38 0.92 144 7.5 164.02 0.31 77 15 14 2.53 0.15 61 25 10 1.00 0.092 92 30 8 0.63 0.077 121

Table 1 can be used to compute critical length with any combination ofECB 10× rating and wire gauge. As an example for a 15 A breaker using 16AWG wire:

ECB Rating AWG MOhms/foot Critical resistance Critical length 15A 16 .020.15 37 feetSuggesting if electronic circuit breaker results in a hard trip, thefault is within 37 feet of wire.

Example 2 Using Inductor di/dt Method

The experimental set up was 17 feet of 14 AWG wire. The inductance ofAWG 14 wire was measured to be 283.8 nH per foot. The 17 feet of AWG 14wire had an inductance of 4.82 μH and R_(wire) was 0.067 ohm. Thevoltage source delivered 28V DC. For the purposes of initial evaluationit was assumed that a typical aircraft AC voltage source appears as a DCsource for the duration of the di/dt events described herein. The halfcycle time of the 400 Hz source frequency is 1.25 ms which is muchgreater than the typical range for the time content of LR circuit (<10μS) Behavior of the setup can be predicted by using previously derivedequations. di/dt rise time vs. distance to fault when R_(arc)=0 ohm isillustrated in graph form in FIG. 9.

The FIG. 9 distance to fault graph is a non-linear curve with a maximumresolution (change in di/dt per foot) of 3.9 amps/μSec per foot at 5feet and a minimum resolution of 0.006863 amps/μSec per foot at 120feet. The percent error in computing distance to fault for the abovesetup with 17 feet of AWG 14 wire is given by Equation 10 and plotted onFIGS. 10A and 10B. These graphs are plotted for different value ofinitial load current (0, 5, 10, 20 amps). On FIG. 10A, R_(arc) is 1 ohmand on FIG. 10B, R_(arc) is 2 ohms.

The percent error graphs show that measured di/dt value will deviate bymore than 15% from ideal at t=1 μsec when R_(arc) is 1 ohm and I_(load)is 0 amp. With increased initial load current the error will increasefurther. The expected di/dt with 17 feet of AWG 14 wire and R_(arc)=0ohm is di/dt=28V/4.8 μH=5.8 A/μSec. FIGS. 11A and 11B show the capturedwaveforms showing the i(t) for the R_(arc)˜0 ohm (FIG. 11A) and 7.5 ohm(FIG. 11B) with I_(load) at 3 amps (FIG. 11A) and 0 amp (FIG. 11B). Withpresence of R_(arc), the di/dt is distorted from ideal. With 7.5 ohmsR_(arc) and 3.0 amps for I_(load), di/dt is measured to be 3.25amps/μSec approximated by a line from 0-1 μSec time period which resultsin a 43% error. When R_(arc) is near 0 ohms, di/dt was measured to be 6Amps/μSec which deviates by 2% from the expected value.

Example 3 Resonant Frequency of LCR Oscillation

The set up included 19 feet and 25 feet of 14 AWG wire. The inductanceof the AWG 14 wire was 283.8 nH per foot. The 19 feet of AWG 14 wire hadan inductance of 5.62 μH with R_(wire)=0.072 ohm. The 25 feet of AWG 14wire had an inductance of 7.09 μH of inductance with R_(wire)=0.145 ohm.The voltage source was DC at 28V with L_(decoupling)=5 mH. It wasassumed that the typical aircraft AC voltage source may be considered aDC source for the LCR oscillation events evaluated. The half cycle timeof a 400 Hz source frequency is 1.25 ms which is much greater than thetypical duration of an LCR oscillation, which is typically 20-30 μSec.

The initial value for C_(out) was 9.89 nF forcing the LCR resonantfrequency range to be around 272 kHz-1.3 MHz for AWG 14 wire of 5 ft-120ft distance range. There was a significant decay in amplitude ofoscillation of the captured waveforms indicating that energy wasdissipated elsewhere in the circuit (most likely through theL_(decoupling) and source). Choosing a smaller value of C_(out), andcorresponding higher frequency range, has a number of advantages. Itprovides greater change in frequency per foot (Δω_(o)/ft), reduces the %Error that can potentially be introduced by R_(arc) as seen fromEquation 20, and increases the Critical Resistance value. A higherfrequency range will also allow longer oscillation time (less energy isleaked through L_(decoupling)) which results in higher signal to noiseratio in frequency domain. At higher resonant frequencies we can keepL_(decoupling) relatively small, saving space and reducing powerdissipation of the ECB. But these advantages will come at the expense ofincreased hardware complexity (faster A/D converters, larger storagememory, longer processing time, etc). Also, a smaller value for C_(out)can potentially increase the effect of an error introduced by parasiticcapacitance of the harness that appears in parallel to C_(out).

The experiment was repeated with C_(out) of 2.17 nF forcing thefrequency range to be 585 kHz-2.86 Mhz with improved results. The datathat follows relates to this latter case. Before data collection,behavior of the set up was estimated using the above formulas. The worsecase critical resistance point occurs with minimum inductance wire at 5ft. From Equation 15, this is equal to 51.0 ohms. In other words, inorder for the oscillation to occur on the entire distance range (5ft-120 ft) of the AWG 14 wire the series resistance R_(arc)+R_(wires)(or simply ˜R_(arc)) must be less than 51.0 ohm. Frequency range vs.distance to fault is plotted on FIG. 12 and is given by f_(o)=ω_(o)/2π.The frequency vs. distance graph is a non-linear curve with greatestchange in frequency per foot being 284.5 kHz/ft at 5 feet and thesmallest being 2.4 kHz/ft at 120 feet with an assumption that thetypical harness length on an aircraft is between 5 and 120 feet.

Expected resonant frequency at 25 feet is 1/(7.09 μH*2.17nF)^(0.5)=8.06*10⁶ rad/sec=1.283 MHz. Expected critical resistance at 25feet is 114.3 ohms.

Expected resonant frequency at 19ft. is 1/(5.62 μH*2.17nF)^(0.5)=9.05*10⁶ rad/sec=1.442 MHz. Expected critical resistance at 19ft is 101.8 ohms.

If we assume that the R_(arc) is zero ohms, the percent error incomputing the distance to fault is given by Equation 20 and is plottedon FIG. 13.

FIG. 14 displays the arc current, arc voltage and V_(o) at 19 foot (FIG.14A) and 25 foot (FIG. 14B) fault locations. The frequency of theoscillation was measured to be 1.47 Mhz for the 19 foot fault locationand 1.25 Mhz for the 25 foot fault location, with arc resistance near 0ohm. The arc resistance was monitored by monitoring the arc current andthe arc voltage behavior. In order to see the effect of arc resistanceon overall waveform, R_(arc) was adjusted by using low inductance carboncomposition resistors in series with an arc itself. Increasing R_(arc)also increases the arc voltage. FIGS. 15A, 15B and 15C display theobtained waveforms from the 25 ft fault locations.

Although an expected critical resistance for R_(arc) is above 100 ohms,the waveforms (FIGS. 15A, 15B and 15C) illustrate that at 30 ohms of arcresistance the oscillation is already severely damped. At R_(arc)=30ohms, the percent error in resonant frequency and corresponding distanceto fault is minimal, less than 5%. The measured frequency of resonantoscillation was 1.25 Mhz, slightly less than the expected value of 1.28Mhz, resulting in 2.3% error. An observed sharp decay in amplitude ofthe captured waveforms cannot be entirely attributed to the in-seriesarc and wire resistance only. Energy stored in the LCR loop has manyways of escaping. Some of it is dissipated through L_(decoupling) andeventually through the source itself. Although L_(coupling) presentsrelatively large impedance to LCR loop for our frequency range, aportion of the energy will inevitably be dissipated through it.Furthermore, inductance of the L_(coupling) is not a fixed value. Asharp rise of short circuit current that the arc creates will start tosaturate the core of the L_(copuling) causing its inductance and thusits impedance to drop. This effect further dampens the amplitude of theresonant oscillation.

Given the nature of the high current arc, at the instant when a faultoccurs, the arc voltage does not always drop to zero volts in a stepfunction. A zero volt arc voltage drop is usually a brief short circuitcondition during the arc fault event. On a microscopic scale, motion onthe faulty wires, vibration forces, melting and rapid evaporation ofmetal all have a direct effect on behavior of the arc voltage and thusarc resistance Waveforms on FIG. 16 show the arc current and arc voltagecaptured during one of the parallel arc faults on a 19 foot arc faultlocation. In this example, the arc voltage drops exponentially from theinstant a fault occurs rather than in a step. Arc resistance follows thesame curve dropping to about 1.3 ohms when oscillation occurs. In caseslike this, where the arc resistance R_(arc) does not drop in a stepfunction from infinite to zero, the damping factor will be increased(and no longer be a static parameter) effectively reducing the amplitudedecay rate. However, the drop of R_(arc) is fast enough to have aminimum effect on the resonant frequency of oscillation. V_(o) waveformshows that the frequency of oscillation is still 1.42 Mhz which iswithin 1% of the expected frequency.

FIG. 17 illustrates another example of captured waveform where arcvoltage behaves irregularly before dropping to 0 volts. LCR oscillationoccurs 20 μSec from the instant of arc strike. The amplitude ofoscillation is significantly lower than in previous cases. This isexpected since initial energy stored in C_(out) is dissipated by an arcprior to the actual oscillation event. In all the cases, with the set upused, presence of LCR oscillation will occur if the arc resistancerapidly drops below 30 ohms at some point during arc fault event.

Frequency content of the captured waveforms can be examined by applyinga fast fourier transform analysis (FFT). FIG. 18 shows an FFT waveformobtained from the time domain waveforms of FIG. 14B and FIG. 19 shows anFFT waveform obtained from the time domain waveforms of FIG. 15B. Thesampling rate used to generate these waveforms was 10 Ms/s andcorresponds to general mid to upper range A/D converters on the market.The FIG. 18 waveform shows FFT of the frequency waveform where R_(arc)is near 0 ohm. The FIG. 19 waveform shows FFT of the waveform withR_(arc)=15 ohms. The frequency peak occurs at 1.29 Mhz and is clearlyvisible in both, however there is at least 14 dB reduction in magnitudedue to 15 ohms added arc resistance.

FIGS. 20, 21 and 22 show FFT (on right hand side) for several randomwaveforms of V_(o) (on left hand side) obtained at a 25 foot arc faultlocation. FFT was applied to the “raw” signal without anypreconditioning or filtering. The sample size for the FFT covers theentire waveform in a time domain as shown on the left. The frequencypeak value in all of the waveforms was 1.30 Mhz which is within 2% ofthe expected value. FIG. 20 illustrates rapid voltage noise prior tooscillation. FIG. 21 illustrates rapid voltage noise introduced halfwaythrough the signal producing broad frequency noise around the resonantfrequency. FIG. 22 illustrates a relatively weak signal.

FFT effectively isolates the frequency of interest from the backgroundnoise induced by the sporadic behavior of the arc voltage and can serveas one of the methods of determining the frequency in real time. Itsperformance can be improved by limiting the scan region to include onlythe location where actual LCR oscillation occurs. Simplest way toachieve that is by introducing a band-pass filter at the input tuned tothe frequency range of interest. Analog band pass filter at the inputwill attenuate all the frequencies outside the expected range improvingthe FFT performance.

One or more embodiments of the present invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention.Accordingly, other embodiments are within the scope of the followingclaims.

What is claimed is:
 1. A method to measure a distance to an arcemanating from a wire having a voltage source and electronic circuitbreaker at a first end thereof and a load at a second end thereof,comprising the steps of: obtaining an output voltage, V₀, of saidvoltage source and a peak current, I_(arc(peak)), of said circuit;calculating a resistance of said wire up to said arc from:R _(wires) =V ₀ /I _(arc(peak)); and utilizing an inherent resistanceper unit of length of said wire to determine a distance from saidvoltage source to said arc.
 2. The method of claim 1 wherein said wireis bundled in a wiring harness having a plurality of parallel runningwires and said wiring harness is installed on an aircraft.
 3. The methodof claim 2 wherein said arc extends from said wire to a second wire andR_(wires) is the sum of the resistance of said wire and said second wirefrom said voltage source to said arc.
 4. The method of claim 2 includingcalculating a Critical Length of said wire beyond which a short circuitcurrent drops below a 10x rating for said electronic circuit breakerwhereby if said electronic circuit breaker trips, then said distance tosaid arc is less than said Critical Length.
 5. The method of claim 2wherein said arc extends from said wire to an airframe of said aircraftand R_(wires) is the resistance of said wire from said voltage source tosaid arc.
 6. The method of claim 1, wherein V_(o) is obtained bymeasuring the output voltage of the electronic circuit breaker.
 7. Themethod of claim 1, further comprising estimating an error in saiddistance determination, by assuming a value for resistance of said arcR_(arc); and calculating the error as R_(arc)/R_(wires), the error beingexpressed as a percentage.
 8. The method of claim 1, further comprisingestimating an error in said distance determination, by estimating an arccurrent I_(arc); assuming a value for resistance of said arc R_(arc);and calculating the error as I_(arc)*R_(arc)/V₀, the error beingexpressed as a percentage.
 9. The method of claim 8, further comprisingusing the value of I_(arc(peak)) for I_(arc) to estimate a minimumerror.
 10. The method of claim 8, further comprising assuming R_(arc)=0;and calculating a critical length of said wire in accordance with thewire gauge and a rating value for said circuit breaker.
 11. The methodof claim 10, wherein the critical length for said wire gauge is thelength for which a hard fault results in an I²t trip at the circuitbreaker.